On the Adjustment of Combined GPS/Levelling/Geoid Networks
A detailed and statistically rigorous treatment of adjustment problems in combined GPS/levelling/geoid networks is given in this paper. The two main types of ”unknowns” in this kind of multi-data ID networks are the gravimetric geoid accuracy and a 2D spatial field that describes all the systematic distortions among the available height data sets. An accurate knowledge of the latter becomes especially important when we consider employing GPS techniques for levelling purposes with respect to a local vertical datum. Various modeling alternatives for the correction field are presented, namely a pure discrete deterministic model, a hybrid deterministic and stochastic model, and finally a pure stochastic model. Variance component estimation is also introduced as an important tool for assesing the actual geoid noise level, and checking a-priori given geoid error models. In addition, theoretical comparisons are made with some of the already established adjustment models that have been used in practice. The problem of statistical testing of various model components (data noise, deterministic model, stochastic model) in such networks is also discussed. Finally, some conclusions are drawn and a few recommendations for further study are pointed out.